In recent years, attention has been given to the development of single-core and multi-core optical fibers for use as fiber optic shape sensors in a variety of applications. The terms “single-core” and “multi-core” refer to the number of light-guiding cores contained within a surrounding reflective cladding material of a length of fiber optic cable. That is, a single-core optical fiber has a single light-guiding core contained within the reflective cladding of the cable, while a multi-core optical fiber typically has a plurality of substantially identical cores each purposefully arranged in the cladding material. Lengths of optical fibers can be configured with specialized strain sensors and attached to or embedded within a surface of an object, with the various strain measurements used to calculate or estimate the shape of the object.
For example, sensors known as Fiber Bragg Gratings can be formed by laser-inscribing, writing, or otherwise embedding a periodic variation of refractive index into the cores of the optical fiber, thus effectively creating an in-line optical filter designed to block particular wavelengths of light transmitted through or along the core. Likewise, Rayleigh scatter detectors can be used to detect elastic light scatter occurring within a core at specific axial locations of the optical fiber. Using these and/or other strain sensors, the bending geometry at each co-located strain sensor can be determined, with this data used in various ways to approximate the shape of an object to which the cable is attached, or within which the cable is embedded.
When a multi-core fiber optic cable in particular is subjected to bending, the strain imposed in each core depends on the curvature of the bend, the direction of the bend, and the arrangement of the various constituent cores within the cable in relation to the direction of the bending. In accordance with linear elastic tube theory, a light-guiding core positioned on the inside of a bend experiences a stress, i.e., a negative strain, while a core positioned on the outside of the bend experiences a positive strain. The amount of strain is proportional to the bend radius and the position of each core relative to the center of the bend curve. Therefore, multi-core fibers can have additional utility in comparison to single core fibers when used for structural shape sensing and end effecter tracking.
However, conventional fiber optic shape sensing methodologies can be error prone, and therefore can produce less than optimal results. Common methods, including those outlined by S. Klute et al. in “Fiber Optic Shape Sensing & Distributed Strain Measurements on a Morphing Chevron,” 44th American Institute of Aeronautics and Astronautics (AIAA) Aerospace Sciences Meeting & Exhibit, #AIAA 2006-624, Jan. 9-12, 2006, Reno, Nev. These methods are highly dependent on the accuracy of successive strain measurements, which are used to calculate the bending parameters of the length of cable at discrete segments thereof. How a particular shape measurement system uses such incrementally-calculated bending parameters to determine shape and end position of a fiber optic cable determines to a large extent the contribution or import of strain measurement error to the final shape determination.
That is, estimated bending parameters of each segment of the cable, or more particularly of each light-guiding core within the optical fiber portion of the cable, are used to discretely determine the location of the next segment, beginning with a calibrated section of cable having a “true” or calibrated spatial location. The strain error at each point along a length of the core or cores is thus directly summed into the final end position measurement, with any twisting of the core or cores in conjunction with the twisting of a bonded protective outer jacket or sleeve exacerbating the error in the calculations, thus leading to less than optimal shape determination.